Question

find the number of years required to reach the intended future value at the given rate: p=$7000, FV=$10000, r=4.3%

Answer 1

Given :

p =$7000,

A = $10000,

r = 4.3% = 0.043

Assume a simple interest

$\begin{gathered} A=P+I \\ I=P\cdot r\cdot t \\ A=P+P\cdot r\cdot t \\ A=P\cdot(1+r\cdot t) \end{gathered}$

So,

$\begin{gathered} A=P\cdot(1+r\cdot t) \\ 10000=7000\cdot(1+0.043\cdot t) \end{gathered}$

Solve for t :

$\begin{gathered} 10000=7000\cdot(1+0.043\cdot t) \\ 1+0.043\cdot t=\frac{10000}{7000}=\frac{10}{7} \\ 0.043\cdot t=\frac{10}{7}-1 \\ \\ 0.043t=0.42857 \\ \\ t=\frac{0.42857}{0.043}\approx9.97 \end{gathered}$

So, rounding to the nearest year

So, time = 10 years

​